We have a basket and a hat.
The basket has the numbers 1, 2, 3, 4 and 5.
The hat contains the letters A, B, C and D.
We have to calculate the probabiltiy of drawing a number that is greater than 3 from the basket and drawing the letter C from the hat.
We have two events:
- Drawing a number greater than 3 from the basket
- Drawing a C from the hat
They are independent as the probability of each on does not depend on the outcome of the other event.
Then, we can calculate the probability of the two events happening together as the product of its probabilities:
[tex]P(n>3&l=C)=P(n>3)\cdot P(l=C)[/tex]The probability of drawing a number greater than 3 can be described as 2/5, as we have 2 numbers greater than 3 (4 and 5) out of 5 numbers in the basket.
The probability of drawing a letter C can be described as 1/4, as we have one letter C out of 4 letters available.
Then, we can calculate the probability as:
[tex]\begin{gathered} P(n>3&l=C)=P(n>3)\cdot P(l=C) \\ P(n>3&l=C)=\frac{2}{5}\cdot\frac{1}{4}=\frac{2}{20}=\frac{1}{10} \end{gathered}[/tex]Answer: the probability is 1/10 or 0.1.
What is the solution of x^2+3x-28
Let's solve for x by factoring this quadratic equation.
We first need to determine which two numbers multiply to -28 (c) but add to 3 (b).
The two numbers that multiply to -28 and add to 3 are 7 and -4.
Therefore, we can factor this equation like so:
[tex](x+7)(x-4)[/tex]Now, we can set this equation to 0 and solve for x.
[tex](x+7)(x-4)=0[/tex]If we look at each factor individually, we can determine the values of x:
[tex](x+7)=0[/tex]Subtract 7 from both sides of the equation.
[tex]x=-7[/tex]Now, let's look at the other factor:
[tex](x-4)=0[/tex]Add 3 to both sides of the equation.
[tex]x=4[/tex]The solution of x^2 + 3x - 28 is x = -7, x = 4.
what property of parallel lines is illustrated by where the snow has collected?
Okay, here we have this:
Considering that when two parallel lines are intersected by a transversal, corresponding angles have the same measure. In this case
Mr. Lambert borrows $900 from a credit union to buy a new laptop. The credit union charges 6.5 % simple interest per year. How much interest will he owe if it takes him 18 months to repay the loan? Round to the nearest cent.
$87.75
Step-by-step explanation:
900×6.5%×18months
=58.5×1.5years
=87.75
slove 2/3 + 5/6 in its simplest term
We solve as follows:
[tex]\frac{2}{3}+\frac{5}{6}=\frac{3}{2}[/tex]Help me please and give me easy way how to solve
To solve for the value of x in the length of a rectangle:
[tex]\begin{gathered} \text{Length = (2x+1)cm} \\ \text{width = 12cm} \\ \text{Area is not less than 108cm}^2 \end{gathered}[/tex]Area of a rectangle = length x width , If the area of a rectangle is less than 108 thus the value is greater than 108cm²
[tex]\begin{gathered} \text{Area of a rectangle = length x width } \\ A=\text{ L X W} \\ A>\text{ L x W} \end{gathered}[/tex][tex]\begin{gathered} (2x+1\text{ x 12)>108} \\ 24x+12>108 \\ 24x>108-12 \\ 24x>96 \\ x>\frac{96}{24} \\ x>4 \end{gathered}[/tex]Hence the correct answer for the value of x > 4
The value of x is less than 4
What is an Area?
An object's Area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
According to the question,
Length = (2x+1) cm
Width = 12 cm
To solve , the Area of the rectangle = length x width i.e.
less than 108 cm^2
length x width = (2x+1) x 12 cm
Area < 108 cm^2
So,
(2x+1) x 12 < 108
2x+1 < 108/12
2x+1 < 9
2x < 8
x < 4
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Kenya is driving on the highway at a speed of 75 mph. She sees an accident about 500 feet ahead and must come to a complete stop. How far will Kenya travel before coming to a complete stop? Answer to the nearest hundredth of a foot. (Use rule of thumb for reaction time: 1 foot traveled for each mile per hour of speed.)
The distance Kenya travels before coming to a complete stop found by writing equations is 425 feet
What is an equation?An equation is a mathematical statement that connects two expressions with an equal sign
The speed at which Kenya is driving = 75 mph
The distance between Kenya and the accident = 500 feet
The rule of thumb for the reaction distance = 1 ft per mile per hour of speed
The rule of thumb expressed as an equation is therefore;
Distance traveled during the reaction time = 1 × v
Where;
v = The speed of driving
The distance Kenya traveled before reacting is therefore;
r = 1 ft/mph × 75 mph = 75 feet
The distance Kenya traveled before stopping is therefore;
500 feet - 75 feet = 425 feet
500 feet – 75 feet = 425 feet
The distance Kenya travels before coming to a complete stop is 425 feet’
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find the area of the equilateral triangle. round to the nearest tenth
the The area of the triangle is 35.1
We can get the height of the triangle using Pythagorean theorem
a^2+b^2=c^2
the height is 7.8
the area of the triangle is 1/2 * base * height
1/2 * 9 *7.8 = 35.1
What is the area of the entire rectangle?
triangles?
square units
6.2 in.
8 in.
square units What is the area of one of t
Answer:
Step-by-step explanation:
Area of the triangle is:
A = 1/2 * (Base * Height)
A = 1/2 * (b * h)
A = 1/2 * (8 * 6.2)
A = 1/2 * 49.6
A = 24.8
Area of the rectangle is
A = Base * Height
A = b * h
A = 8 * 6.2
A = 49.6
who found roman numerals?
Answer: the ancient Romans
Step-by-step explanation:
Answer:
Step-by-step explanation:
jefferson thompson made the numberal numerebaals
Britta made her last monthly interest-only payment on may 5. her next
payment is due on june 5. what will be the amount of that interest-only
payment?
The amount of that interest-only payment is $21.53.
Define interestsThe term "interest" refers to the extra money an investor makes on top of their investment or the extra money a borrower owes on top of the money they've been loaned. Along with the loan itself, there is an additional sum or interest that must be paid.
Interests come in two types: simple interest and compound interest.
Given,
She has been awarded a $6,000 for 10-year federal loan at 4.29%.
First interest-only payment was done on May 5.
So, on June 5 second interest-only payment is done.
Interest she paid on May 5 is,
First Interest = [tex]\frac{6000*4.29}{12*100}[/tex]
= [tex]\frac{25740}{1200}[/tex]
= $21.45
Thus, the balance after the first interest = $6000 + $21.45
= $6021.45
Interest she paid on June 5 is,
Second Interest = [tex]\frac{6021.45*4.29}{12*100}[/tex]
= [tex]\frac{25832.02}{1200}[/tex]
= $21.53
Thus, the amount of that interest-only payment is $21.53.
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The correct question is:
Britta has been accepted into a 2-year medical assistant program at a career school. She has been awarded a $6,000 unsubsidized 10-year federal loan at 4.29%. She knows she has the option of beginning repayment of the loan in 2.5 years. She also knows that during this nonpayment time, interest will accrue at 4.29%. Britta made her last monthly interest-only payment on May 5. Her next payment is due on June 5. What will be the amount of that interest-only payment?
What is the formula for figuring out how far the students walked?
37.
Add all the distances .
3/4 + 1/2 + 2/3 + 3/4 = 8/3 miles
To add fractions you need equal bottom numbers
find the LCM ( Least common multiple of the denominators )
4 , 2 , 3 , 4 = LCM = 12
Multiply each fraction by the same numerator and denominator, to obtain 12 as a bottom number
(3/4 * 3/3) + (1/2 * 6/6) + (2/3 * 4/4) + (3/4 * 3/3)
9/12 + 6/12 + 8/12 + 9/12
Now that all fractions have the same denominator ( bottom number) you can add them.
Add the numerators ( top numbers ) and put 12 as a denominator.
(9 + 6 + 8 + 9 ) / 12 = 32/12
Simplify ( divide both numbers by 4 )
32/12 = 8/3
2(x2 - 4x) + 5(x + 1)x(2x + 1) - (4x - 5)(x² - 6x + 7) - (x² - 14x + 13)x(3x - 4) - 3(x² + 2) + 122x(x + 1) + x(x + 1)4(x+ - 1.5x) + 2(x? - 3)8x - 62x2 - 3x + 5Don
Starting with the first expression:
[tex]\begin{gathered} (x^2-6x+7)-(x^2-14x+13) \\ \Rightarrow x^2-6x+7+x^2+14x-13 \\ \text{collect like-terms} \\ x^2+x^2-6x+14x-13+7 \\ \Rightarrow2x^2+8x-6 \\ \\ \text{This is not the answer, as it is not the same with the two(2) expressions given in the solution} \end{gathered}[/tex]Simplifying the second expression:
[tex]\begin{gathered} 2(x^2-4x)+5(x+1) \\ \Rightarrow2x^2-8x+5x+5 \\ \Rightarrow2x^2-3x+5 \\ \\ \text{This expression is equal to the option B} \end{gathered}[/tex]Simplifying the third expression:
[tex]\begin{gathered} x(2x+1)-(4x-5)_{} \\ \Rightarrow2x^2+x-4x+5 \\ \Rightarrow2x^2-3x+5 \\ \\ \text{This expression is also equal to option B} \end{gathered}[/tex]Simplifying the fourth expression:
[tex]\begin{gathered} x(3x-4)-3(x^2+2)+12x \\ \Rightarrow3x^2-4x-3x^2-6+12x \\ \Rightarrow3x^2-3x^2-4x+12x-6 \\ \Rightarrow8x-6 \\ \\ \text{This is correct for option A} \end{gathered}[/tex]Simplifying the last expression:
[tex]\begin{gathered} x(x+1)+x(x+1)-4(x^2-1.5x)+2(x^2-3) \\ \Rightarrow x^2+x+x^2+x-4x^2+6x+2x^2-6 \\ \Rightarrow x^2+x^2-4x^2+2x^2+x+x+6x-6 \\ \Rightarrow8x-6 \\ \\ \text{This expression is also true for option A} \end{gathered}[/tex]Seeds cost for a farmer are 40$ per acre for corn and 30$ per acre for soybeans . How many acres of each crop should the farmer plant if she wants to spend no more than 2400 on seed? Express your answer as a liner inequality with appropriate nonnegative restrictions and draw its graph
Given that:
- The seeds cost is 40$ per acre for corn.
- The seeds cost is 30$ per acre for soybeans.
- The farmer wants to spend no more than $2400.
• Let be "x" the number of acres of seeds for corn and "y" the number of acres of seeds for soybeans.
You know that the total amount of money has to be less than or equal to $2400. Therefore, you can write the following Linear Inequality to represent that situation:
[tex]40x+30y\leq2400[/tex]You can rewrite it in another form by solving for "y":
[tex]\begin{gathered} 30y\leq-40x+2400 \\ \\ y\leq\frac{-40x}{30}+\frac{2400}{30} \end{gathered}[/tex][tex]y\leq-\frac{4}{3}x+80[/tex]Since the number of acres cannot be negative:
[tex]\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}[/tex]• You can identify that the boundary line is:
[tex]y=-\frac{4}{3}x+80[/tex]It is written in Slope-Intercept Form:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case, you can identify that the y-intercept is:
[tex]b=80[/tex]In order to find the x-intercept, substitute this value of "y" into the equation and solve for "x" (because the y-value is zero when the line intersects the x-axis):
[tex]y=0[/tex]Then, you get:
[tex]0=-\frac{4}{3}x+80[/tex][tex]\frac{(-80)(3)}{-4}=x[/tex][tex]x=60[/tex]You can identify that the symbol of the inequality is:
[tex]\leq[/tex]It indicates that the line must be solid and the shaded region must be below the boundary line.
Knowing all this information, you can graph the inequality on the Coordinate Plane (Remember that the values of the variables must be greater than or equal to zero. Then, you must shade with a different color the region in which "x" and "y" are greater than or equal to zero).
Hence, the answer is:
- Linear Inequality:
[tex]40x+30y\leq2400[/tex]- Nonnegative restrictions:
[tex]\begin{gathered} x\ge0 \\ y\ge0 \end{gathered}[/tex]- Graph:
Please help me with this problem I keep getting this wrong an my son is not understanding clearly.Use the parabola tool to graph the quadratic function. f(x)=3x^2 + 6x − 24 Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
The general vertex-equation of a parabola has the following form:
[tex]f(x)=a\cdot(x-h)^2+k.[/tex]Where:
• a is a multiplicative factor,
,• (h, k) are the coordinates of the vertex of the parabola.
In this exercise we have the following equation:
[tex]f(x)=3\cdot x^2+6x-24.[/tex]Vertex of the parabola
To find the vertex of the parabola, we will complete squares to take the equation f(x) to the general form as in the equation above.
i. We factorize the equation of f(x) in the following way:
[tex]f(x)=3\cdot(x^2+2x)-24.[/tex]ii. Now, we rewrite the term inside the parenthesis as:
[tex]\begin{gathered} f(x)=3\cdot(x^2+2\cdot1\cdot x)-24 \\ =3\cdot((x^2+2\cdot1\cdot x+1)-1)-24 \\ =3\cdot(x^2+2x+1)-3-24 \\ =3\cdot(x^2+2x+1)-27. \end{gathered}[/tex]iii. Now, we see that the term in parenthesis can be rewritten as a square:
[tex]f(x)=3\cdot(x+1)^2-27.[/tex]iv. Finally, we rewrite the term inside and outside the parenthesis as:
[tex]f(x)=3\cdot(x-(-1))^2+(-27).[/tex]In the last step, we rewrite the term inside the parenthesis to have the same shape as in the general expression.
Comparing the equation that we have obtained and the general one, we see that the coordinates of the vertex are:
[tex](h,k)=(-1,-27).[/tex]Second point
We find a second point by evaluating the function f(x) in x = 1, we get:
[tex]f(1)=3\cdot1^2+6\cdot1-24=3+6-24=-15.[/tex]The coordinates of the second point are (1, -15).
Graph
We have the following points of the parabola:
[tex]\begin{gathered} \text{ Vertex }=(-1,-27), \\ \text{ Second point }=(1,-15). \end{gathered}[/tex]Using these points and taking into account that the axis of symmetry is x = -1 (because the x-coordinate of the vertex is -1), we get the following graph:
AnswerCoordinates of the vertex: (-1, -27)
Coordinates of the second point: (1, -15)
Answer the question for me please and explain how you got the answer
Given:
a.) y = 2.5 when x = 9
Let's find the constant of variation (k).
For us to be able to determine which of the given choices is the answer, let's plugin x = 2.5 and y = 9 in each of them to see if it will make the equation correct.
CHOICE A: k = 22.5 ; y = 22.5x
2.5 = 22.5(9)
2.5 ≠ 202.5 (False)
Choice A is not the answer
CHOICE B: k = 3.6 ; xy = 3.6
(2.5)(9) = 3.6
22.5 ≠ 3.6 (False)
Choice B is not the answer
CHOICE C: k = 3.6 ; y = 3.6/x
2.5 = 3.6/9
2.5 ≠ 0.4 (False)
Choice C is not the answer
CHOICE D: k = 22.5 ; xy = 22.5
(2.5)(9) = 22.5
22.5 = 22.5 (True)
Choice D is the answer
Therefore, the answer is CHOICE D.
Consider the function f(x)=2(3)x.
What are the coordinates of the y-intercept of the function?
The coordinates of the y-intercept of the function is (0, 2)
How to determine the coordinates of the y-intercept?The equation of the function is given as
f(x) = 2(3)x
The equation is an exponential function
So, we need to represent it properly
The equation of the function is:
f(x) = 2(3)ˣ
Next, we set the x-coordinate to 0
So, we calculate the y-intercept
f(0) = 2(3)⁰
Evaluate the equation
f(0) = 2
This means that the y-intercept of the function is (0, 2)
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Mindy gets 3 dollars a week for allowance. She saved all of her allowance for 10 weeks, and then she bought a shirt for 24 dollars. How much money did
she have left?
Answer:
$6 left
Step-by-step explanation:
since she saved up for 10 weeks= 3*10
$30-$24(price of the shirt)
=$6
How far from the base of a wall must a
17-foot ladder be placed in order to
reach the top of a 12-foot wall.
The 12.04m is far from the base to wall.
How to calculate far from the base of the wall??The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the number system whose digits are used to represent numbers and the number system in which logarithms are defined.
Let the base of the 17ft long ladder be placed x ft away from the wall so that it exactly reaches the top of a 12- foot tall wall.
By Pythagorean theorem
12²+X²=17²
x²=17²-12²=145
x=√145=12.04
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The accompanying graph shows the heart rate, in the beats per minute, of a jogger during a 4 minute interval. What is the rage of the jogger's heart rate during this interval?
The range of the jogger's heart rate is defined by the interval from the minimum value to the maximum value, where we can have values in the y-axis.
Looking at the graph, the minimum heart rate is 60 bpm, and the maximum is 110 bpm, and we can have any value inside this interval.
So the range is:
[tex]\text{range}=\lbrack60,110\rbrack[/tex]For the number line shown which statement is not true?
|d| <|c|
Ic
|c|>c
|d| = d
Answer:
The answer is C
Step-by-step explanation:
it's always the one in the lines at least that's what my math teacher told me he said it's really easy All you have to do is pick the ones with the lines there's more to it when you're doing homework but when there's just like a few questions it's way easier
You decide to invest $10,000 in an account where the interest compounds annually. Create an exponential function to represent how much money you will have after 20 years if the money grows at a rate of 7.5 percent
Apply the compound interest formula:
• A= P (1 + r/n)^nt
Where:
A = future value
P = Principal investment = $10,000
r = interest rate in decimal form = 7.5 /100 = 0.075
n= number of compounding periods per unit t = 1 (anually)
t= years = 20
Replacing:
A = 10,000 ( 1+ 0.075 )^20
A survey estimates the current average cost of college to be $34,179.
(a) If the average cost of college increased by 7.4% each year, what will be the average cost of college 15 years from now?
(b) If a savings plan offers a rate of 5.4% compounded continuously, how much should be put in the plan now to pay for 1 year of college 15 years from now?
(Round to the nearest cent as needed)
so for the trouble this is the last one. and thank everyone for your help.
Simplify the following complex rational expression completely. Detailed Step By Step
Given:
[tex]\frac{\frac{1}{7}+\frac{1}{x}}{\frac{x}{7}-\frac{7}{x}}[/tex]Let us write the numerator as a single fraction, as well as the denominator. This can be written as:
[tex]\frac{\frac{x+7}{7x}}{\frac{x^2-49}{7x}}[/tex]Division by a fraction may become a mu
[tex]\begin{gathered} \frac{x+7}{7x}\times\frac{7x}{x^2-49} \\ \\ =\frac{x+7}{7x}\times\frac{7x}{(x+7)(x-7)} \\ \\ =\frac{1}{x-7} \end{gathered}[/tex]I need to know the answer to this problem... 3/4(x-8)=-1/2
Answer: x=22/3
Step-by-step explanation: Combine multiplied terms into a single fraction. Distribute. Multiply all terms by the same value to eliminate fraction denominators. Cancel multiplied terms that are in the denominator. Multiply the numbers. Add 24 to both sides. Simplify. Divide both sides by the same factor. Simplify.
Write an equation in Standard Form that passes through the point (-8, 7) and has a slope of -3.
Answer:
3x+y=-17
Step-by-step explanation:
Standard form is written as: Ax+By=C where the slope is always -A/B
-A/B = -3/1
A= 3 and B=1
3x+y=C
Plug in point to solve for C
3(-8)+7=C
-24+7=C
-17=C
3x+y=-17
Find slope for (19,-2),(-11,10)
Answer:
-2/5
Step-by-step Explanation:
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]m = \frac{10 - ( - 2)}{ - 11 - 19} [/tex]
[tex]m = \frac{12}{ - 30} [/tex]
[tex]m = - \frac{2}{5} [/tex]
The cost in dollars) of producing a high-end plasma television sets is C = g(2) = 550 + 402. Find a formula for the inverse function g'.g-'(C)=
Given:
The function is,
[tex]g(x)=550+40x[/tex]Explanation:
Assume y = g(x). So
[tex]\begin{gathered} y=g(x) \\ =550+40x \end{gathered}[/tex]Replace variable x with y and y with x.
[tex]x=550+40y[/tex]Solve the equation for y.
[tex]\begin{gathered} x=550+40y \\ 40y=x-550 \\ y=\frac{x-550}{40} \end{gathered}[/tex]So inverse of function g(x) is,
[tex]g^{-1}(x)=\frac{x-550}{40}[/tex]Bill is trying to plan a meal to meet specific nutritional goals. He wants to prepare a meal containing rice, tofu, and peanuts that will provide 283 grams of carbohydrates, 391 grams of fat, and 197 grams of protein. He knows that each cup of rice provides 50 grams of carbohydrates, 0 grams of fat, and 1 grams of protein. Each cup of tofu provides 4 grams of carbohydrates, 13 grams of fat, and 20 grams of protein. Finally, each cup of peanuts provides 35 grams of carbohydrates, 73 grams of fat, and 31 grams of protein. How many cups of rice, tofu, and peanuts should he eat?
♥Answer:
♥Bill needs to eat 5 Cups of rise, 1 cup of tofu and 4 cups of peanuts
♥Explanation:
♥Its simple calculations:
♥As Bill requirement is 350 grams of carbohydrates, 311 grams of Fats and 168 gram of proteins.
♥Each cup of rice provides 42 grams of carbohydrates, 0 grams of fat, and 1 gram of protein.
♥Each cup of tofu provides 4 grams of carbohydrates, 11 grams of fat, and 23 grams of protein.
♥Each cup of peanuts provides 34 grams of carbohydrates, 75 grams of fat, and 35 grams of protein.
♥If he eats 5 cups of rise than he gets 42 × 5 = 210 grams of carbohydrates. similarly he gets 0 × 5 = 0 grams of fats and 1 × 5 = 5 grams of proteins.
♥If he eats 1 cup of tofu than he gets 4 × 1 = 4 grams of carbohydrates. similarly he gets 11 × 1 = 11 grams of fats and 23 × 1 = 23 grams of proteins, and If he eats 4 cups of peanuts than he gets 34 × 4 = 136 grams of carbohydrates. Similarly he gets 75 × 4 = 300 grams of fats and 35 × 4 = 140 grams of proteins.
♥GRAND TOTAL BECOMES
♥CARBOHYDRATES: 210+4+136=350 grams
♥FATS: 0+11+300= 311 grams
♥PROTEINS:5+23+140=168 grams♥
Find the 52nd term. 22, 30, 38, 46,…
Given a series.
22, 30, 38, 46,…
use the formula,
a+(n-1)d,
a= 22
n=52
d=8.
subsitute in the formula,
22+(52+1)8
=22+424
=446